I am not into the theory, but in practice the ITIN application will be rejected if credit for other dependent box is not check, or the credit is not claimed. The IRS rejection notice says:

We rejected your return because:

- You weren't listed on an attached U.S. federal income tax return, or

- You were listed as a dependent n an attached U.S. federal income tax return but were not claimed for any allowable tax benefit.

The PTO software does not do either of the two.

I contacted PTO. Initially they said as they always say that software was written according to the IRS rules, then I point out that the IRS will not reject its own rules, then they say they will look into it. I found it is very hard to follow up with the issue since there is no case management system accessible to customers, I do not know what you have looked, and what they have decided to do. The lack of track-abilities of the issues we reported is a major problem, all the software companies I know of, and some non-software companies as well, can manage the life cycle of a case.